Ratio and Proportion Examples With Answers, deals with various concepts which are as under:-

- Converting Ratios to Simplest Form
- Equivalent Ratios
- Find the numbers when their ratio and sum are given
- Divide sum of money between two persons when ratio are given
- Divide sum of money among 3 persons when ratio are given
- Are the given number are in proportion
- Find the value of y when four numbers are in proportion

**Ratio and Proportion Examples With Answers – Convert Ratio into its simplest form**

In order to convert the given ratio to Simplest Form, we should follow the following steps : –

- Find the HCF of both the numerator and denominator
- Dividing Both numbers by their HCF

The result is the ratio in its simplest form.

**Example 1**

Convert the ratio 60 : 35 in its simplest form.

**Solution**

HCF of 60 and 35 is 5

Since, 60 : 35

=

Dividing Both 60 and 35 by their HCF

=

=

= 12 : 7

Hence, the simplest form of 60 : 35 is 12 : 7

**Ratio and Proportion Examples With Answers – Equivalent ratios**

In order to find Equivalent Ratios of any given ratio, we multiply or divide the numerator and denominator of the ratio by the same non zero number.

**Example 2**

Find the Equivalent ratio of 2 : 3

, , ,

**Solution**

On multiplying or dividing each term of a ratio by the same non zero number, we get a ratio equivalent to the given ratio

For,

Both numerator and denominator of given fraction is multiplied by same nonzero number i.e 4

=

is an equivalent ratio of

is not an equivalent ratio of As both 2 and 3 are not multiply by same non zero number

is not an equivalent ratio of As both 2 and 3 are not multiply by same non zero number

is not an equivalent ratio of As both 2 and 3 are not multiply by same non zero number

**Ratio and Proportion Examples With Answers – Find the numbers when their ratio and sum are given**

**Example 3**

Two numbers are in the ratio 3 : 5 and their sum is 160. Find the numbers?

**Solution**

Let the required number be 3a and 5a

Since the sum of these two numbers is given, we can say that

3a + 5a = 160

8a = 160

a =

a = 20

So, the first number is 3a = 3 x 20

= 60

Second number is 5a = 5 x 20

= 100

Hence, two numbers are 60 and 100

**Ratio and Proportion Examples With Answers – Divide sum of money between two persons when ratio are given**

**Example 4**

Divide ₹ 6000 among X and Y in the ratio 1 : 4

**Solution**

Total money = ₹ 6000

Given ratio = 1 : 4

Sum of ratio terms = ( 1 + 4 ) = 5

Give: part of ₹ 6000 to X

Give: part of ₹ 6000 to Y

that is,

X ‘s share = ₹ ( 6000 x ) = ₹ 1200

Y ‘s share = ₹ ( 6000 x ) = ₹ 4800

**Ratio and Proportion Examples With Answers – Divide sum of money among 3 persons when ratio are given**

**Example 5**

Divide ₹ 1800 among X , Y and Z in the ratio 3 : 4 : 1

**Solution**

Total money = ₹ 1800

Given ratio = 3 : 4 : 1

Sum of ratio terms = ( 3 + 4 + 1 ) = 8

X share = ₹ ( 1800 x ) = ₹ 675

Y share = ₹ ( 1800 x ) = ₹ 900

Z share = ₹ ( 1800 x ) = ₹ 225

**Ratio and Proportion Examples With Answers – Comparison of ratios**

To Compare two Ratios, we should follow the following steps : –

- Write both the Ratios as Fractions
- Convert both the Fractions into Like Fraction:-

– Find the L.C.M of denominator of both the Fractions

– Make the denominator of each fraction equal to their L.C.M. - In case of Like fractions, the number whose numerator is greater is larger.

**Example 6**

Compare the ratios ( 2 : 5 ) and ( 3 : 4 )

**Solution**

We can write

( 2 : 5 ) = and ( 3 : 4 ) =

Now, let us compare and

LCM of 5 and 4 is 20

Making the denominator of each fraction equal to 20

We have, = =

and = =

In case of Like fractions, the number whose numerator is greater is larger. Hence we can say <

That is <

Hence, ( 2 : 5 ) < ( 3 : 4 )

__Ratio and Proportion Examples With Answers – Four Numbers in Proportion__

Let a, b, c, d are four numbers said to be in proportion.

then, a : b = c : d or a : b :: c : d

here a and d are called the extreme terms or extremes.

b and c are called the middle terms or means.

When Four numbers are in proportion

then, **Product of extremes = Product of means.
**i.e, In proportion a : b :: c : d,

(a x d) = (b x c)

**Ratio and Proportion Examples With Answers – Are the given number are in proportion**

**Example 7**

Are 8 , 6 , 12 , 6 in proportion?

**Solution**

As we Know,

Product of extremes = Product of means

Here, Means are 6 and 12

Extremes are 8 and 6

Product of extremes = 8 x 6 = 48

Product of means = 6 x 12 = 72

Since, Product of extremes ≠ Product of means

Hence, 8 , 6 , 12 , 6 are not in Proportion

**Ratio and Proportion Examples With Answers – Find the value of y when four numbers are in proportion**

**Example 8**

If 6 : 9 : : y : 15, find the value of y?

**Solution**

We know that, Product of means = Product of extremes

In the given numbers, we can say that 9 , y are means and 6 , 15 are extremes

9 x y = 6 x 15

y =

y = 10

Hence, y = 10

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